Comments on Maximum Likelihood Estimation and Projections Under Multivariate Statistical Models

Filipiak, Katarzyna; John, Mateusz; Markiewicz, Augustyn

doi:10.1007/978-3-030-56773-6_4

Cited by 5 publications

(2 citation statements)

References 27 publications

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“…The estimator P C (S 2 ) is unbiased, explicit, and consistent. Moreover, from Filipiak et al (2020), it is known that the projection S 1 on the quadratic subspace Ψ C is also the maximum likelihood estimator. Moreover, if we project a positive definite matrix on a quadratic subspace, then its condition number does not increase (see Markiewicz and Mieldzioc (2023)).…”

Section: Orthogonal Projectionmentioning

confidence: 99%

“…The standard maximum likelihood estimator can be given in explicit form only for structures belonging to quadratic subspaces (see Filipiak et al (2020), Szatrowski (1980)). If this assumption is not satisfied, then it is still possible to compute the maximum likelihood estimator, but numerical methods must be involved.…”

Section: Constrained Maximum Likelihood Estimationmentioning

confidence: 99%

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Estimation methods for a linearly structured covariance matrix

Mieldzioc

2023

Biometrical Letters

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Summary Covariance matrices with a linear structure are widely used in multivariate analysis. The choice of the most appropriate covariance structure can be made from a class of possible linear structures. Once we have made the choice, an important question is how we can estimate the covariance matrix for a given covariance structure. This article describes methods used to estimate the structured covariance matrix, and indicates the advantages and disadvantages of the selected methods.

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Section: Orthogonal Projectionmentioning

confidence: 99%

Section: Constrained Maximum Likelihood Estimationmentioning

confidence: 99%

Estimation methods for a linearly structured covariance matrix

Mieldzioc

2023

Biometrical Letters

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Testing independence under a block compound symmetry covariance structure

2022

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Testing covariance structures belonging to a quadratic subspace under a doubly multivariate model

Filipiak,

John,

Liang

2024

TEST

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A hypothesis related to the block structure of a covariance matrix under the doubly multivariate normal model is studied. It is assumed that the block structure of the covariance matrix belongs to a quadratic subspace, and under the null hypothesis, each block of the covariance matrix also has a structure belonging to some quadratic subspace. The Rao score and the likelihood ratio test statistics are derived, and the exact distribution of the likelihood ratio test is determined. Simulation studies show the advantage of the Rao score test over the likelihood ratio test in terms of speed of convergence to the limiting chi-square distribution, while both proposed tests are competitive in terms of their power. The results are applied to both simulated and real-life example data.

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Comments on Maximum Likelihood Estimation and Projections Under Multivariate Statistical Models

Cited by 5 publications

References 27 publications

Estimation methods for a linearly structured covariance matrix

Estimation methods for a linearly structured covariance matrix

Testing independence under a block compound symmetry covariance structure

Testing covariance structures belonging to a quadratic subspace under a doubly multivariate model

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